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Simplifying -29x2 + -48x + -13 = 0 Reorder the terms: -13 + -48x + -29x2 = 0 Solving -13 + -48x + -29x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 48x + 29x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 48x + 29x2)' equal to zero and attempt to solve: Simplifying 13 + 48x + 29x2 = 0 Solving 13 + 48x + 29x2 = 0 Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. 0.4482758621 + 1.655172414x + x2 = 0 Move the constant term to the right: Add '-0.4482758621' to each side of the equation. 0.4482758621 + 1.655172414x + -0.4482758621 + x2 = 0 + -0.4482758621 Reorder the terms: 0.4482758621 + -0.4482758621 + 1.655172414x + x2 = 0 + -0.4482758621 Combine like terms: 0.4482758621 + -0.4482758621 = 0.0000000000 0.0000000000 + 1.655172414x + x2 = 0 + -0.4482758621 1.655172414x + x2 = 0 + -0.4482758621 Combine like terms: 0 + -0.4482758621 = -0.4482758621 1.655172414x + x2 = -0.4482758621 The x term is 1.655172414x. Take half its coefficient (0.827586207). Square it (0.6848989300) and add it to both sides. Add '0.6848989300' to each side of the equation. 1.655172414x + 0.6848989300 + x2 = -0.4482758621 + 0.6848989300 Reorder the terms: 0.6848989300 + 1.655172414x + x2 = -0.4482758621 + 0.6848989300 Combine like terms: -0.4482758621 + 0.6848989300 = 0.2366230679 0.6848989300 + 1.655172414x + x2 = 0.2366230679 Factor a perfect square on the left side: (x + 0.827586207)(x + 0.827586207) = 0.2366230679 Calculate the square root of the right side: 0.486439172 Break this problem into two subproblems by setting (x + 0.827586207) equal to 0.486439172 and -0.486439172.Subproblem 1
x + 0.827586207 = 0.486439172 Simplifying x + 0.827586207 = 0.486439172 Reorder the terms: 0.827586207 + x = 0.486439172 Solving 0.827586207 + x = 0.486439172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.827586207' to each side of the equation. 0.827586207 + -0.827586207 + x = 0.486439172 + -0.827586207 Combine like terms: 0.827586207 + -0.827586207 = 0.000000000 0.000000000 + x = 0.486439172 + -0.827586207 x = 0.486439172 + -0.827586207 Combine like terms: 0.486439172 + -0.827586207 = -0.341147035 x = -0.341147035 Simplifying x = -0.341147035Subproblem 2
x + 0.827586207 = -0.486439172 Simplifying x + 0.827586207 = -0.486439172 Reorder the terms: 0.827586207 + x = -0.486439172 Solving 0.827586207 + x = -0.486439172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.827586207' to each side of the equation. 0.827586207 + -0.827586207 + x = -0.486439172 + -0.827586207 Combine like terms: 0.827586207 + -0.827586207 = 0.000000000 0.000000000 + x = -0.486439172 + -0.827586207 x = -0.486439172 + -0.827586207 Combine like terms: -0.486439172 + -0.827586207 = -1.314025379 x = -1.314025379 Simplifying x = -1.314025379Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.341147035, -1.314025379}Solution
x = {-0.341147035, -1.314025379}
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